The odds of getting a perfect NCAA bracket are way better than 1 in 9,223,372,036,854,775,808

YouTube

Professor Jeff Bergen explains the simple math.

March Madness is around the corner, and the NCAA men's basketball tournament bracket was just released.

Now it's time for millions of basketball fans and office workers across the country to fill out their brackets and try to guess which team is going to win it all this year.

So, what are your odds of actually getting a perfect bracket and correctly predicting every game in the tournament?

1 in 9,223,372,036,854,775,808

At a first glance and taking the most naive approach to the tournament, the odds are somewhere around 1 in 9.2 quintillion.

Before the 2012 tournament, DePaul University math professor Jeff Bergen posted a video on YouTube explaining where this number comes from.

There are 63 total games in a tournament bracket. For each of those games, two teams play, and one team wins. So, filling out a bracket consists of picking 63 winners.

So, you have two options for the first game, two options for the second game, two options for the third game, and so on, for all 63 games. To get the total number of possible ways to fill out a bracket, you multiply together all 63 of these twos, giving us 2⁶³, or 9,223,372,036,854,775,808 possible brackets.

If all of these brackets are equally likely - if each game in the entire tournament is a 50-50 tossup, and picking the winner is basically a coin flip - we then get the odds of a correct bracket at one in 9.2 quintillion.

Actually, it's more like 1 in 576,460,752,303,423,488

Of course, flipping a coin 63 times is probably not a very good strategy for deciding how to fill out your bracket. Most of the games are not 50-50 matchups.

Consider the first round (the round of 64) of the NCAA Tournament. Of the 32 games in the first round, there are four games in which four of the best 64 teams (1^st seeds) play four of the worst 64 teams (16^th seeds).

Since 1985, when the tournament first expanded to 64 teams, no 16^th seed has ever beaten a 1^st seed in the round of 64.

If we're comfortable assuming that this trend continues, we can safely fill in the four 1^st seed vs. 16^th seed games on our brackets.

Now we have 59 games to pick, and if we flip coins for all those, we have a one in 2⁵⁹, or one in 576,460,752,303,423,488, chance of winning the tournament. Still pretty terrible odds, but by making this one assumption, we have boosted our chances by a factor of 16.

Or maybe it's more like 1 in 128 billion

Professor Bergen suggests that by taking a more nuanced approach to the tournament along these lines and factoring in ratings and seedings, we can improve our odds to around one in 128 billion.

That is still insanely unlikely - you are about 500 times more likely to win the lottery.

Watch Bergen's video here: